On the Expectation-Maximization Unfolding with Smoothing

TL;DR

This paper develops error propagation formulas for a regularized unfolding algorithm, introduces an Akaike information criterion-based method for selecting smoothing parameters, and evaluates its performance and coverage through simulations.

Contribution

It presents a novel approach to automatic smoothing parameter selection in unfolding using AIC, with a detailed analysis of bias and uncertainty implications.

Findings

AIC effectively guides smoothing parameter choice.

The method maintains good frequentist coverage.

Unfolding bias and uncertainty are systematically analyzed.

Abstract

Error propagation formulae are derived for the expectation-maximization iterative unfolding algorithm regularized by a smoothing step. The effective number of parameters in the fit to the observed data is defined for unfolding procedures. Based upon this definition, the Akaike information criterion is proposed as a principle for choosing the smoothing parameters in an automatic, data-dependent manner. The performance and the frequentist coverage of the resulting method are investigated using simulated samples. A number of issues of general relevance to all unfolding techniques are discussed, including irreducible bias, uncertainty increase due to a data-dependent choice of regularization strength, and presentation of results.